Scanning probe microscope and method

ABSTRACT

An interfacial force microscope includes a differential-capacitance displacement sensor having a tip mounted on an oscillating member. The sensor generates displacement signals in response to oscillations of the member. A scanner is adjacent the sensor and supports a sample to be imaged. The scanner is actuable to move the sample relative to the sensor to bring the tip into intermittent contact with said sample as the member oscillates. A controller is in communication with the sensor and the scanner. The controller includes a sensor feedback circuit receiving the displacement signals and an AC setpoint signal. The AC setpoint signal has a frequency generally equal to the frequency at the peak of the displacement versus frequency curve of the sensor. The output of the sensor feedback circuit is applied to the sensor to oscillate the member. The controller also provides output to the scanner in response to the displacement signals to control the separation distance between the sensor and the sample.

FIELD OF THE INVENTION

The present invention relates generally to imaging and in particular toa method and apparatus for intermittent contact imaging.

BACKGROUND OF THE INVENTION

Atomic-force microscopy has become widely used to image surfaces ofsamples on a microscopic scale. Its popularity to a large extent is dueto the fact that an atomic-force microscope (AFM) measures the force orforce gradient between a sharp tip disposed on a cantilever and a samplesurface at a picoNewton (pN) level as opposed to the tunneling currentmeasured with a scanning tunneling microscope (STM). This of courseallows the AFM to image insulating as well as conducting samples.

AFMs can be operated in either contact or intermittent contact modes.When operating in a contact mode, the deflection of a weak cantilever iskept constant while servoing the vertical extension of a piezoelectricscanner supporting the sample being imaged. The piezoelectric scanner isalso rastered in an x-y plane to scan the surface of the sample. A mapof the vertical extension of the piezoelectric scanner at various x,ycoordinates of the sample surface, which is assumed to be proportionalto a change in voltage on the piezoelectric scanner, reflects thetopography of the sample surface. Unfortunately, problems exist in thatsoft samples are often damaged by the plowing action of the tip on thesample as the sample is rastered by the piezoelectric scanner in the x-yplane.

When operating in an intermittent contact mode, the base of a stiffcantilever is driven by a piezoelectric element which induces anoscillation at the free end of the cantilever. By driving the cantilevernear its resonant frequency, an oscillation amplitude ranging from 20 to100 nm at the free end of the cantilever can be achieved. This amplituderange is sufficient to inhibit the tip from sticking to the samplesurface during each contact. To generate the image, the verticalextension of the piezoelectric scanner is servoed to maintain a constantdrop in the oscillation amplitude. The piezoelectric scanner is alsorastered in an x-y plane to scan the surface of the sample. In order toachieve high sensitivity, a high quality factor (Q) is necessary.Tapping mode cantilevers typically have Q values ranging from 100 to1000 in air.

To enhance the measurement of force displacement curves, a modified formof atomic-force microscopy, referred to as interfacial force microscopy,has been developed. Interfacial force microscopes (IFMs) replace thecantilever with a differential-capacitance displacement sensor. Feedbackis used to servo the net electrostatic torque of the sensor such that itcancels the torque resulting from tip-sample forces. As a consequence,the tip support remains at its rest position throughout the forceprofile. This feature eliminates the snap-to-contact instability whichplagues weak cantilevers in the attractive force regime and correlatesthe tip-sample deformation directly to the vertical extension of thepiezoelectric scanner in nanoindentation studies.

Feedback attempts to inhibit the common plate of the displacement sensorfrom actually deflecting which leads to rapid restabilization of thedisplacement sensor after hard collisions with pronounced surfacefeatures. However, this places considerable demands on the rate at whichforce signals drift since it is often necessary to image a large fieldof view at a slow lateral scan. Generally, a contact force in the rangeof 200 nN corresponds to a force signal in the order of 10 mV. As willbe appreciated, the force signal has very little room to drift over thescan duration. A slow drift in the attractive force direction results ina slight increase in the contact force applied to the sample over thescan. Drifts in the repulsive force direction can pull the piezoelectricscanner completely out of feedback. Accordingly, improved imagingtechniques are desired.

It is therefore an object of the present invention to provide a novelmethod and apparatus for intermittent imaging.

SUMMARY OF THE INVENTION

According to one aspect of the present invention there is provided anapparatus for intermittent contact imaging comprising:

-   -   a sensor to contact intermittently a sample to be imaged and        generating displacement signals during oscillation thereof;    -   a scanner adjacent said sensor and supporting said sample to be        imaged, said scanner being actuable to move said sample relative        to said sensor to bring said sensor into intermittent contact        with said sample; and    -   a controller in communication with said sensor and said scanner,        said controller including a sensor feedback circuit receiving        said displacement signals and an AC setpoint signal, said AC        setpoint signal having a frequency generally equal to the        frequency at the peak of the displacement versus frequency curve        of said sensor, the output of said sensor feedback circuit being        applied to said sensor to oscillate the same, said controller        further providing output to said scanner in response to said        displacement signals to control the separation distance between        said sensor and said sample.

According to another aspect of the present invention there is providedan interfacial force microscope comprising:

-   -   a differential-capacitance displacement sensor having a tip        mounted on an oscillating member, said sensor generating        displacement signals during oscillation of said member;    -   a scanner adjacent said sensor and supporting a sample to be        imaged, said scanner being actuable to move said sample relative        to said sensor to bring said tip into intermittent contact with        said sample and to move said sample relative to said sensor to        raster said sensor over said sample; and    -   a controller in communication with said sensor and said scanner,        said controller including a sensor feedback circuit receiving        said displacement signals and an AC setpoint signal, said AC        setpoint signal having a frequency generally equal to the        frequency at the peak of the displacement versus frequency curve        of said sensor, the output of said sensor feedback circuit being        applied to said sensor to oscillate said member, said controller        further providing output to said scanner in response to said        displacement signals to control the separation distance between        said sensor and said sample.

According to still yet another aspect of the present invention there isprovided a method of imaging a sample surface comprising the steps of:

-   -   oscillating a sensor at a driven setpoint frequency to cause        said sensor to intermittently contact a sample to be imaged;    -   generating displacement signals in response to oscillations of        said sensor;    -   moving the sample relative to said sensor to maintain the        separation distance between said sensor and sample; and    -   rastering said sensor over the sample surface, wherein said        driven setpoint frequency is generally equal to the frequency at        the peak of the frequency versus displacement curve of said        sensor.

The present invention provides advantages in that soft samples can beimaged on a microscopic level using a highly damped sensor whilereducing the shear forces applied to the sample as the sample isscanned.

BRIEF DESCRIPTION OF THE DRAWINGS

An embodiment of the present invention will now be described more fullywith reference to the accompanying drawings in which:

FIG. 1 is a schematic block diagram of an interfacial force microscopeunder force-feedback control configured to operate in an intermittentcontact mode;

FIG. 2 is another schematic block diagram of the interfacial forcemicroscope of FIG. 1 showing further detail;

FIG. 3 is yet another schematic block diagram of the interfacial forcemicroscope of FIG. 1 showing further detail;

FIG. 4 is an enlarged, exploded perspective view of adifferential-capacitance displacement sensor forming part of theinterfacial force microscope of FIG. 1;

FIG. 5 is a schematic block diagram of a force-feedback controllerforming part of the interfacial force microscope of FIG. 1;

FIG. 6 is a block circuit diagram of a PID controller forming part ofthe force-feedback controller of FIG. 5;

FIG. 7 shows a 1 kHz intermittent contact image of Kevlar fiber-epoxytaken using the interfacial force microscope of FIG. 1;

FIG. 8 shows another 1 kHz intermittent contact image of Kevlarfiber-epoxy taken using the interfacial force microscope of FIG. 1highlighting a damaged area; and

FIG. 9 shows graphs illustrating the magnitude and phase of therelationship between the ratio of V_(demod) and V_(aux) as a function offrequency when the differential-capacitance displacement sensor isoperated in air;

FIG. 10 shows graphs illustrating the magnitude and phase of therelationship between the ratio of V_(PID) and V_(aux) as a function offrequency when the differential-capacitance displacement sensor isoperated in air;

FIG. 11 shows graphs illustrating the magnitude and phase of therelationship between the open loop gain GOL as a function of frequencywhen the differential-capacitance displacement sensor is operated in airwith the curves of FIG. 8 superimposed thereon; and

FIG. 12 shows intermittent contact images of the surfaces of Hexadecane(3.34 cP) and Glycerol (1490 cP).

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

Referring now to FIG. 1, an interfacial force microscope (IFM) underforce-feedback control and configured to operate in an intermittentcontact mode to generate microscopic images of a sample underobservation in accordance with the present invention is shown and isgenerally indicated to by reference numeral 20. As can be seen, the IFM20 includes a differential-capacitance displacement (DCD) sensor 22 tocontact intermittently the sample to be imaged. A controller 24 iscoupled to the DCD sensor 22 as well as to a piezoelectric scanner 26positioned adjacent the DCD sensor 22 and supporting the sample. Thepiezoelectric scanner 26 is responsive to the controller 24 to move thesample in a vertical direction to alter the sensor-sample separation.The piezoelectric scanner 26 is also actuable to move the samplelaterally in an x-y plane to raster the DCD sensor 22 over the sample ata rate equal to about 2 to 3 μm/s. An imager 27 such as a NanoScope IIIaMultiMode manufactured by Digital Instruments receives output from thecontroller 24 and generates surface images of the sample. The controller24 drives the DCD sensor 22 such that it operates in an intermittentcontact mode while maintaining a high quality factor Q. The qualityfactor Q is of a value to achieve sufficient sensor output displacementsignal contrast between out of contact and contact conditions of the DCDsensor 22 and the sample even though the DCD sensor is highly damped inair. Further details of the IFM 20 and in particular, the force-feedbackcontrol will now be described.

FIGS. 2 and 3 better illustrate the IFM 20. As can be seen, thecontroller 24 includes a force-feedback (FFB) controller 24 a and animage feedback (IFB) controller 24 b. FFB controller 24 a is responsiblefor driving the DCD sensor 22 and includes a feedback circuit tuned toestablish a well defined peak within the displacement-frequency spectrumof the DCD sensor 22 sufficient to achieve the desired high qualityfactor Q. The IFB controller 24 b is responsible for servoing thevertical extension of the piezoelectric scanner 26 to control thesensor-sample separation at each x,y coordinate of the sample beingintermittently contacted by the DCD sensor 22. The FFB controller 24 bis connected to the DCD sensor 22 directly as well as through apreamplifier 28. The preamplifier 28 has a high input impedance toinhibit excessive loading on the DCD sensor 22.

An amplitude and phase detector 30, a function generator 32, anoscillator 34 and optionally a volt meter 36 are also connected to theFFB controller 24 a. The IFB controller 24 b is connected to theamplitude and phase detector 30 and provides output to thepiezo-controller 26 a of the piezoelectric scanner 26. Thepiezo-controller 26 a in turn drives the piezoelectric tube 26 b of thepiezoelectric scanner in the z-direction to alter the sensor-sampleseparation.

A multi-channel analog to digital converter (ADC) 44 is connected to theIFB controller 24 b, the FFB controller 24 a and the amplitude and phasedetector 30. The ADC provides the output to the imager 27. An optionaloscilloscope 46 is connected to the FFB and IFB controllers 24 a and 24b respectively.

Turning to FIGS. 2 to 4, the DCD sensor 22 is better illustrated. As canbe seen, the DCD sensor 22 includes a stainless steel orBeryllium-Copper (BeCu) common plate 50. A common plate 52 having a pairof torsion bars 54 extending in opposite directions from its sides isdefined by a cut 56 in the common plate 50. The common plate 52 isdisposed above a pair of gold or chromium electrodes 58 mounted on aquartz substrate 60. A tip 62 is attached to the common plate 52 by wayof a conductive adhesive to help to reduce the mass of the DCD sensor22. The tip 62 is fashioned from a wire having a diameter equal to about0.125 mm by electrochemical etching and has a parabolic profile. Thecommon plate 52 is connected to the input of the preamplifier 28.

The electrodes 58 are dc biased and are driven by RF driving signalsoutput by the FFB controller 24 a. The RF driving signals are 180degrees out of phase and have a frequency well beyond the mechanicalbandwidth of the DCD sensor 22 (i.e. 1 MHz) to establish an RFcapacitance bridge defined by the electrodes 58 and common plate 52 thatis sensitive to changes in capacitance at an aF level. The electrodes 58are also driven by an AC setpoint signal generally in the range of fromabout 1 kHz to 1.5 kHz which causes the common plate 52 to oscillate aswill be described. The frequency of the AC setpoint signal is a functionof the mechanical properties of the DCD sensor material, its dimensionsetc.

When the tip 62 encounters the sample supported by the piezoelectricscanner 26, a force is applied to the tip 62 resulting in torque beingapplied to the common plate 52. The applied torque causes the commonplate 52 to rotate. Rotation of the common plate 52 changes thecapacitance between the electrodes 58 and the common plate 52 and isdetected by the RF capacitance bridge. When the common plate 52 rotatesby a small angle θ≈δ/L where δ is the change in the average gap betweenthe common plate 52 and one of the electrodes 58 and L is the distancebetween the mid-point of the torsion bar axis and the tip 62, adisplacement signal appears on the common plate 52. The displacementsignal has an amplitude equal to 2ΔCV_(ac)/C_(Total), where ΔC is thechange in capacitance, V_(ac) is the amplitude of the RF driving signalsand C_(Total) is equal to two times the capacitance between the commonplate 52 and one electrode 58 plus any stray capacitance in parallelwith the DCD sensor 22. The displacement signal has a frequency equal tothe frequency of the RF driving signals and a phase dependent on thedirection of rotation of the common plate 52. The displacement signal onthe common plate 52 is picked up by the preamplifier 28, amplified andconveyed to the FFB controller 24 a.

FIG. 5 better illustrates the FFB controller 24 a. As is shown, FFBcontroller 24 a includes a demodulator 70 receiving the displacementsignal output of the preamplifier 28 and the RF signal output of thefunction generator 32. The demodulator 70 demodulates and low passfilters the displacement signal output of the preamplifier 28 togenerate demodulator amplitude signal output V_(demod). The demodulatorsignal output V_(demod) is applied to the amplitude and phase detector30 and to a PID controller 72. The PID controller 72 also receives theAC setpoint signal output of the oscillator 34 and generates V_(PID) and−V_(PID) feedback signals. The −V_(PID) feedback signal is conveyed toone of the channels of ADC 44 and to the oscilloscope 46 while theV_(PID) feedback signal is conveyed to an RF PID controller 74. The RFPID controller 74 also receives a DC voltage and the RF signal output ofthe function generator 32 from the demodulator 70 and supplies the RFdriving signals to each of the electrodes 58.

The PID controller 72 is better illustrated in FIG. 6 and as can beseen, it includes a summing amplifier 80 having unity gain. The summingamplifier receives the demodulator signal output V_(demod) as well asthe AC setpoint signal V_(aux) from oscillator 34. The sum output of thesumming amplifier 80 is therefore −(V_(aux)+V_(demod)) and representsthe error signal for the DCD sensor feedback loop. The sum output of theamplifier 80 is applied to a proportional-integral-derivative (PID)control block 82. The PID control block 82 has a good low frequencyresponse and provides output proportional to the combination of itsinput, the time integral of its input and the time rate of change of itsinput. The output of the PID control block 82 is conveyed to a pair ofsumming amplifiers 84 and 86 functioning as high-pass filters, oneamplifier 84 of which generates the V_(PID) feedback signal and theother amplifier 86 of which generates the −V_(PID) feedback signal.Since the summing amplifier 80 has unity gain, the gain G_(PID) from theinput of the PID control block 82 to the output of the summing amplifier84 can be expressed as:G _(PID)=−(G _(P) +G _(I) +G _(D))where:

-   -   G_(P) is the proportional gain and is equal to −1;    -   G_(I) is the integrator gain and is equal to j/wT_(I);    -   G_(D) is the derivative gain and is equal to        G_(D)=−Γ[jωT_(D)/(1+jωT_(D))] over the frequency range of        interest;    -   T_(I) is the time constant of the integrator;    -   T_(D) is the time constant of the differentiator; and    -   Γ represents the gain at the end of the high-pass filter        circuit.        The gain term G_(PID) allows the frequency response of the DCD        sensor feedback loop to be tailored.

If the frequency of the AC setpoint signal V_(aux) is near dc, thesetpoint signal V_(aux) acts as the driven setpoint of the DCD sensorcausing the DCD sensor 22 to oscillate physically such that theresulting feedback signal V_(demod) output by demodulator 70 cancels thesetpoint signal V_(aux). In this case, the resulting error signal−(V_(aux)+V_(demod)) is basically equal to zero. When the AC setpointsignal V_(aux) is moved to higher frequencies, the feedback system isunable to offset the AC setpoint signal V_(aux) resulting in errorsignals which can be quite large.

Prior to imaging, the electronic gains of the integrator anddifferentiator of the PID controller 72 are adjusted such that thesensor displacement signal is nearly in-phase with the AC setpointsignal V_(aux) at the frequency where the open loop gain falls to one(1). In other words, the feedback system has very little phase marginbefore it becomes unstable. However, the feedback system exhibits a muchhigher quality factor Q then if operated without feedback. The PIDcontroller gain adjustments are chosen to obtain a quality factor Q highenough to be sensitive to perturbations caused by the tip striking thesample but not so large that noise becomes an issue. Noise becomes anissue when the quality factor Q is increased to a point where the phasemargin becomes so small that the feedback system edges too close to thebrink of instability.

Once tuning of the PID controller 72 has been completed, thedisplacement vs. frequency plot of the DCD sensor 22 is examined to findthe frequency of maximum displacement. The frequency of the setpointsignal V_(aux) is then set to the frequency of maximum displacement sothat the DCD sensor 22 oscillates at this frequency. At this time, thepiezoelectric scanner 26 is actuated to bring the sample towards the DCDsensor 22 so that the tip 62 intermittently contacts the sample as thecommon plate 52 oscillates. When the tip 62 contacts the sample, theamplitude of the DCD displacement signal decreases.

The amplitude and phase detector 30 applies the amplitude signalV_(demod) to the IFB controller 24 b which in turn outputs a magnitudesignal to the piezo-controller 26 a controlling the piezoelectric tube26 b. The imaging set point is set about 3% lower than the initialoutput of the amplitude and phase detector 30. The piezoelectric scanner26 in turn moves the sample towards the DCD sensor 22 to control theseparation between the tip 62 and the sample such that the displacementsignal of the DCD sensor 22 is constant but lower than the in-air case.During this process, the piezoelectric scanner 26 is rastered in an x-yplane to image the surface of the sample under observation.

The error signals of the piezoelectric scanner feedback loop are appliedto the ADC 44 which also receives phase input from the amplitude andphase detector 30 and the V_(PID) feedback signal from the FFBcontroller 24 a. The digital output of the ADC 44 is conveyed to theimager 27 to allow images to be formed. The error signals of thepiezoelectric scanner feedback loop provide edge-contrast information ofthe sample surface topography while the phase of the displacement signalprovides information related to energy dissipation during tip and samplecontact.

By keeping the mass of the DCD sensor 22 low and establishing a welldefined peak in V_(demod), a high quality factor is maintained. Thisallows the DCD sensor to be operated in an intermittent contact modewhile ensuring sufficient contrast between out of contact and contactdisplacement signals generated by the DCD sensor. As a result, highquality images of the sample under observation can be generated at amicroscopic level.

For a test sample, a fiber composite comprised of Kevlar 49 fibersimbedded in an epoxy matrix (the fiber volume fraction is reported to be50%) was imaged using the IFM 20. Prior to imaging, the sample waspolished. FIG. 7 shows a 1 kHz intermittent contact IFM image (allimages: 180×180 points, plane subtraction, no filtering) of the fibercomposite sample. The ˜50 nm deep polishing grooves are clearly evident,in spite of a maximum height difference of ˜740 nm. The piece of debrisat the left edge remained undisturbed by the imaging procedure. Thetotal imaging time was 11 min, corresponding to 20 contact cycles perpoint.

FIG. 8 shows a 1 kHz intermittent contact IFM image of a badly damagedarea on the Kevlar sample. The massive surface upheaval results in amaximum height difference approaching 3 μm, which deaccentuates theshallow polishing grooves in the unblemished fiber regions. In spite ofthe upheaval, the intermittent contact mode technique had littledifficulty in tracking the surface topography, although optimum imagingrequired doubling the number of contact cycles per point.

To determine the peak contact force during imaging, the separationbetween the tip 62 and a single Kevlar 49 fiber was narrowed until thefirst evidence of intermittent contact was observed, and then thepiezoelectric tube 26 b was advanced until the set point was reached.After dividing the amplitude and phase detector output by theappropriate gain terms, it was estimated that the oscillation amplitudeof the common plate 52 was reduced from 18.97 nm in air to 18.36 nmduring intermittent contact (amplitudes being expressed as peak-to-peakvalues). The distance that the piezoelectric tube 26 b advanced to reachthe set point was 9.9 Å, which is to be compared to the 6.1 Å reductionin the common plate oscillation amplitude.

FIG. 12 shows intermittent contact images of the surfaces of Hexadecane(3.34 cP) and Glycerol (1490 cP). As will be appreciated, the DCD sensor22 can be controlled under force-feedback to image soft as well as hardsamples.

In the intermittent contact mode, the motion of the common plate 52decays only during the contact portion of the cycle. Therefore, thedifference between the advancement of the piezoelectric tube 26 b andthe reduction in common plate oscillation amplitude is a reasonableestimate of the maximum tip-sample deformation, which is about 3.8 Å.

To estimate the peak contact force, the Hertz equation for elasticcontact which is appropriate for axis symmetric parabolic bodies isused: $F = {\frac{4}{3}E*\sqrt{R}*D^{3/2}}$where:R=(1/R _(t)+1/R _(s))⁻¹E^(*) = [(1 − v_(t)²)/E_(t) + (1 − v_(s)²)/E_(s)]⁻¹and is the reduced modulus;

-   -   D is the combined deformation of the tip and sample;    -   V_(t), v_(s) refer to Poisson's ratio;    -   E_(t), E_(s) indicate Young's modulus;    -   R_(t), R_(s) represent parabolic radii of curvature; and    -   t, s denote tip and sample.

To test the sensor feedback loop, the ratio V_(demod)/V_(aux), and theratio V_(PID)/V_(aux), as a function of frequency were measured with theDCD sensor 22 operating in air. It is easy to show that theoreticallyV_(dmod)/V_(aux)=G_(OL)/(1−G_(OL)) and V_(PID)/V_(aux)=G_(PID)(1−G_(OL))where G_(OL)=−G_(PID)G_(force)G_(mech)G_(bridge)G_(preamp)G_(demod) isthe open loop gain, the minus sign being a result of the summingamplifier 80. FIGS. 9 and 10 show how these two ratios vary withfrequency when the DCD sensor 22 operates under the following set ofconditions:T1=4.3×10⁻⁵ s; T _(D)=3.6×10⁻⁵ s; Γ=2.4; and G _(demod)=4.1

G_(demod) is referenced to the peak-to-peak amplitude of thepreamplifier output. The solid line passing through the experimentalpoints is the theoretical result. The level of agreement between theoryand experiment ranges from good to excellent.

Of note in the magnitude plots is the presence of the well-defined peakoccurring around 660 Hz signifying that the sensor feedback loop behavesmuch like a second-order low-pass filter. The origin of this behavior isrooted in Barkhausen's criterion for feedback stability. In other words,the term 1/(1−G_(OL)) tends to infinity if the magnitude of G_(OL)approaches unity and the corresponding phase approaches zero.

FIG. 11 shows the calculated frequency dependence of G_(OL) with themagnitude plot for V_(demod)/V_(aux) superimposed. As can be seen, themagnitude of G_(OL) is roughly 0 dB (or 1) and the corresponding phaseis about 0.08 π at the peak frequency for demodulator output signalV_(demod). The phase margin is small enough to obtain a strong resonanceresponse, but large enough to prevent the sensor feedback loop fromgoing into self-oscillation. It is important to note that a peak in thedemodulator output signal V_(demod) does not mean mechanical resonance.In the example shown, the peak frequency for the demodulator outputsignal V_(demod) is in fact 60 Hz lower than ω₀/2π, the mechanicalresonant frequency of the DCD sensor 22. Nevertheless, a maximum in thedemodulator output signal V_(demod) does mean a maximum in thedisplacement amplitude, but this is not achieved in the usual way.Looking at the magnitude plot for V_(PID)/V_(aux), it can be seen thatthe applied force varies over the frequency range, and reaches a maximumin the vicinity of the peak frequency for the demodulator output signalV_(demod).

A comparison between the phase plots shows that the phase of thedisplacement (or V_(demod)) lags the phase of the force (or V_(PID)) byan angle reasonably close to π/2. This, along with the fact that a 60 Hzdifference in frequency is not very large, suggests that ω₀ does play animportant role in obtaining a strong peak, which can be understood inthe following way. In order to obtain a strong peak and still maintainfeedback stability, one must make G_(I) the dominant electronic gainterm because it is the only electronic gain that rolls off its responsewith increasing frequency, which means that the phase lag due to theelectronics is not far removed from π/2 over the frequency range ofinterest. The mechanical phase lag eventually reaches π/2 at ω₀, whichyields an overall phase lag in the neighborhood of the π phase lagrequired to bring the phase of G_(OL) to zero.

As will be appreciated, the present invention provides advantages inthat samples can be imaged on a microscopic level without damaging thesamples. This makes the present imaging technique particularly suited toimaging soft samples including emulsions and liquids. Images can betaken for several hours without removing the varying de offset in theforce signal which is required during contact mode imaging to ensureminimal contact force between the tip and the sample.

Although the present invention has been described with specificreference to interfacial force microscopy and use of adifferential-capacitance displacement sensor, those of skill in the artwill appreciate that the feedback control used in the preset imagingtechnique can be used with other heavily-damped displacement sensors. Itwill also be appreciated by those of skill in the art, that variationsand modifications may be made to the present invention without departingfrom the spirit and scope thereof as defined by the appended claims.

1-23. (canceled)
 24. A scanning probe microscope apparatus forincreased-quality-factor intermittent contact imaging of a samplesurface comprising: A. a device including 1) a base, 2) a member whichis displaceable relative to the base, 3) a tip mounted on the member tointermittently contact the sample surface to be imaged, and 4) acharacteristic of an inherent/open-loop dynamic compliance functionwhich includes frequency-dependent real and imaginary parts, theinherent/open-loop dynamic compliance function defining aninherent/open-loop quality factor, both the inherent/open-loop dynamiccompliance function and the inherent/open-loop quality factor beingspecific to a reference position at which the tip is physically remotefrom the sample surface; B. means for actuating the member; C. means formeasuring displacements of the member relative to the base andgenerating a displacement signal indicative thereof; D. an oscillatorgenerating a driving signal which includes characteristics of 1) adriving frequency and 2) a driving amplitude, the driving signal causingoscillations in the means for actuating which in turn causes the memberto oscillate which in turn causes the displacement signal to oscillate;E. a feedback controller receiving 1) the displacement signal and 2) thedriving signal and applying an oscillatory actuation signal to the meansfor actuating, the oscillatory actuation signal being mathematicallydependent on 1) the displacement signal, 2) the driving signal, and 3) again function of the feedback controller which generally includesfrequency-dependent real and imaginary parts, the gain function and theinherent/open-loop dynamic compliance function together establishing anoperative/closed-loop resonance condition specific to the referenceposition, the operative/closed-loop resonance condition includingcharacteristics of 1) an operative/closed-loop resonance frequency, 2)an operative/closed-loop resonance amplitude, and 3) anoperative/closed-loop quality factor, the gain function causing apositive phase margin of stability but being such that theoperative/closed-loop quality factor is higher than theinherent/open-loop quality factor, the driving frequency being equal toor near the operative/closed-loop resonance frequency, theoperative/closed-loop resonance amplitude being sufficiently large toprevent the tip from becoming stuck to the sample surface but beingsufficiently small to prevent the sample surface from becomingexcessively damaged while the tip intermittently contacts the samplesurface; and F. a scanner for altering a separation distance between thesample surface and the device in a direction predominantly perpendicularto the sample surface and for imparting relative motions between thesample surface and the device in a plane predominantly parallel to thesample surface.
 25. A scanning probe microscope apparatus in accordancewith claim 24 further comprising: A. an amplitude detector measuring adisplacement amplitude of the displacement signal and generating adisplacement amplitude signal indicative thereof, the displacementamplitude being smaller while the tip intermittently contacts the samplesurface in comparison to when the device is at the reference position;B. a phase detector measuring a phase of the displacement signal withrespect to a reference signal and generating a phase signal indicativethereof; C. means for controlling the scanner including means for 1)receiving the displacement amplitude signal, 2) setting a demandeddisplacement amplitude, 3) controlling the separation distance to bringthe tip into intermittent contact with the sample surface and tomaintain the displacement amplitude in general agreement with thedemanded displacement amplitude while the tip intermittently contactsthe sample, and 4) driving the relative motions to raster scan thesample surface; and D. an imager operatively coupled to 1) the means forcontrolling the scanner, 2) the amplitude detector, and 3) the phasedetector, the imager forming spatially-correlated images derived from 1)the separation distance, 2) a discrepancy between the displacementamplitude and the demanded displacement amplitude, and 3) the phase. 26.A scanning probe microscope in accordance with claim 24 wherein thedisplacements are displacements of translation.
 27. A scanning probemicroscope in accordance with claim 24 wherein the displacements aredisplacements of rotation.
 28. A scanning probe microscope in accordancewith claim 24 wherein the displacements are displacements of bending.29. A scanning probe microscope in accordance with claim 24 wherein thedisplacements are displacements of torsion.
 30. A scanning probemicroscope apparatus in accordance with claim 24 wherein theinherent/open-loop quality factor is indicative of over-dampedoscillations and wherein the inherent/closed-loop quality factor isindicative of under-damped oscillations.
 31. A scanning probe microscopeapparatus in accordance with claim 24 wherein the inherent/closed-loopquality factor is at least one order of magnitude higher than theinherent/open-loop quality factor.
 32. A scanning probe microscopeapparatus in accordance with claim 24 wherein the tip is in a liquidwhen the device is at the reference position and wherein the tip is inthe liquid while the tip intermittently contacts the sample surface. 33.A scanning probe microscope apparatus in accordance with claim 32wherein the liquid includes a characteristic of an absolute viscosity ashigh as 1490 centipoise (cP).
 34. A scanning probe microscope apparatusin accordance with claim 24 wherein the device further includes twostationary electrodes facing the member without contacting the member,the member being electrically conducting to define a pair of variablecapacitors.
 35. A scanning probe microscope apparatus in accordance withclaim 34 wherein the means for actuating includeselectrostatic/capacitive forces.
 36. A scanning probe microscopeapparatus in accordance with claim 34 wherein the means for measuringincludes 1) the pair of variable capacitors, 2) a pair of modulationsignals nominally 180 degrees out of phase with respect to each otherand sufficiently high in frequency to not displace the member relativeto the base, 3) a preamplifier, 4) a demodulator, and 5) a low-passfilter.
 37. A scanning probe microscope apparatus in accordance withclaim 24 wherein the oscillatory actuation signal includes a dccomponent derived from feedback which tends to maintain a constant dclevel of the displacements for all reasonable separation distances. 38.A scanning probe microscope apparatus in accordance with claim 24wherein the tip is of a form appropriate for nanoindentation.
 39. Aninterfacial force microscope for increased-quality-factor intermittentcontact imaging of a sample surface comprising: A. adifferential-capacitance displacement sensor including 1) a base, 2) amember which is rotationally displaceable relative to the base, 3) a tipmounted on the member to intermittently contact the sample surface to beimaged, and 4) a characteristic of an inherent/open-loop dynamiccompliance function which includes frequency-dependent real andimaginary parts, the inherent/open-loop dynamic compliance functiondefining an inherent/open-loop quality factor, both theinherent/open-loop dynamic compliance function and theinherent/open-loop quality factor being specific to a reference positionat which the tip is physically remote from the sample surface; B. meansfor actuating the member via electrostatic/capacitive forces; C. meansfor measuring rotational displacements of the member relative to thebase and generating a displacement signal indicative thereof; D. anoscillator generating a driving signal which includes characteristicsof 1) a driving frequency and 2) a driving amplitude, the driving signalcausing oscillations in the means for actuating which in turn causes themember to oscillate rotationally which in turn causes the displacementsignal to oscillate; E. a force-feedback controller including 1) asumming junction and 2) a control block, the summing junctionreceiving 1) the displacement signal and 2) the driving signal andgenerating an error signal indicative of a discrepancy between thedisplacement signal and the driving signal, the control block receivingthe error signal and applying an oscillatory actuation signal to themeans for actuating, the oscillatory actuation signal beingmathematically dependent on 1) the error signal and 2) a gain functionof the force-feedback controller which generally includesfrequency-dependent real and imaginary parts, the gain function and theinherent/open-loop dynamic compliance function together establishing anoperative/closed-loop resonance condition specific to the referenceposition, the operative/closed-loop resonance condition includingcharacteristics of 1) an operative/closed-loop resonance frequency, 2)an operative/closed-loop resonance amplitude, and 3) anoperative/closed-loop quality factor, the gain function causing apositive phase margin of stability but being such that theoperative/closed-loop quality factor is higher than theinherent/open-loop quality factor, the driving frequency being equal toor near the operative/closed-loop resonance frequency, theoperative/closed-loop resonance amplitude being sufficiently large toprevent the tip from becoming stuck to the sample surface but beingsufficiently small to prevent the sample surface from becomingexcessively damaged while the tip intermittently contacts the samplesurface; and F. a scanner for altering a separation distance between thesample surface and the differential-capacitance displacement sensor in adirection predominantly perpendicular to the sample surface and forimparting relative motions between the sample surface and thedifferential-capacitance displacement sensor in a plane predominantlyparallel to the sample surface.
 40. An interfacial force microscope inaccordance with claim 39 further comprising: A. an amplitude detectormeasuring a displacement amplitude of the displacement signal andgenerating a displacement amplitude signal indicative thereof, thedisplacement amplitude being smaller while the tip intermittentlycontacts the sample surface in comparison to when the device is at thereference position; B. a phase detector measuring a phase of thedisplacement signal with respect to a reference signal and generating aphase signal indicative thereof; C. means for controlling the scannerincluding means for 1) receiving the displacement amplitude signal, 2)setting a demanded displacement amplitude, 3) controlling the separationdistance to bring the tip into intermittent contact with the samplesurface and to maintain the displacement amplitude in general agreementwith the demanded displacement amplitude while the tip intermittentlycontacts the sample, and 4) driving the relative motions to raster scanthe sample surface; and D. an imager operatively coupled to 1) the meansfor controlling the scanner, 2) the amplitude detector, and 3) the phasedetector, the imager forming spatially-correlated images derived from 1)the separation distance, 2) a discrepancy between the displacementamplitude and the demanded displacement amplitude, and 3) the phase. 41.An interfacial force microscope in accordance with claim 39 wherein theinherent/open-loop quality factor is indicative of over-dampedoscillations and wherein the inherent/closed-loop quality factor isindicative of under-damped oscillations.
 42. An interfacial forcemicroscope in accordance with claim 39 wherein the inherent/closed-loopquality factor is at least one order of magnitude higher than theinherent/open-loop quality factor.
 43. An interfacial force microscopein accordance with claim 39 wherein the tip is in a liquid when thedevice is at the reference position and wherein the tip is in the liquidwhile the tip intermittently contacts the sample surface.
 44. Aninterfacial force microscope in accordance with claim 43 wherein theliquid includes a characteristic of an absolute viscosity as high as1490 centipoise (cP).
 45. An interfacial force microscope in accordancewith claim 39 wherein the differential-capacitance displacement sensorfurther includes 1) two oppositely extending torsion bars supporting themember and 2) two stationary electrodes located beneath the memberwithout contacting the member, the member being electrically conductingto define a pair of variable capacitors.
 46. An interfacial forcemicroscope in accordance with claim 45 wherein the means for measuringincludes 1) the variable capacitors, 2) a pair of modulation signalsnominally 180 degrees out of phase with respect to each other andsufficiently high in frequency to not displace the member relative tothe base, 3) a preamplifier, 4) a demodulator, and 5) a low-pass filter.47. An interfacial force microscope in accordance with claim 39 whereinthe control block includes proportional, integral, and derivative gains.48. An interfacial force microscope in accordance with claim 39 whereinthe oscillatory actuation signal includes a dc component derived fromfeedback which tends to maintain a constant dc level of thedisplacements for all reasonable separation distances.
 49. Aninterfacial force microscope in accordance with claim 39 wherein the tipis of a form appropriate for nanoindentation.
 50. A method ofincreased-quality-factor intermittent contact imaging of a samplesurface for a scanning probe microscope apparatus comprised of 1) adevice including i) a base, ii) a member which is displaceable relativeto the base, iii) a tip mounted on the member to intermittently contactthe sample surface, iv) a characteristic of an inherent/open-loopnatural frequency, and v) a characteristic of an inherent/open-loopquality factor, both the inherent/open-loop natural frequency and theinherent/open-loop quality factor being specific to a reference positionat which the tip is remote from the sample surface, 2) means foractuating the member, 3) means for measuring displacements of the memberrelative to the base and generating a displacement signal indicativethereof, 4) an oscillator generating a driving signal which includescharacteristics of i) a driving frequency and ii) a driving amplitude,the driving signal causing oscillations in the means for actuating whichin turn causes the member to oscillate which in turn causes thedisplacement signal to oscillate, and 5) a feedback controller receivingi) the displacement signal and ii) the driving signal and applying anoscillatory actuation signal to the means for actuating, the oscillatoryactuation signal being mathematically dependent on i) the displacementsignal, ii) the driving signal, and iii) a gain function of the feedbackcontroller which generally includes frequency-dependent real andimaginary parts, the method comprising the steps of: A. setting thedriving amplitude above zero and placing the device at the referenceposition; B. while the device is at the reference position: a. measuringa displacement amplitude of the displacement signal for a plurality ofdriving frequencies which include the natural frequency and generatingan operative/closed-loop spectrum of displacement amplitudes versusdriving frequencies, and b. adjusting the gain function in a mannerwhich causes a positive phase margin of stability but produces anoperative/closed-loop resonance peak in the operative/closed-loopspectrum, the operative/closed-loop resonance peak includingcharacteristics of 1) an operative/closed-loop resonance frequency, 2)an operative/closed-loop resonance amplitude, and 3) anoperative/closed-loop quality factor higher than the inherent/open-loopquality factor; c. after adjusting the gain function: a. setting thedriving frequency equal to or near the operative/closed-loop resonancefrequency, and b. setting the driving amplitude such that theoperative/closed-loop resonance amplitude is sufficiently large toprevent the tip from becoming stuck to the sample surface butsufficiently small to prevent the sample surface from becomingexcessively damaged while the tip intermittently contacts the samplesurface; then D. placing the device at an imaging position at which thetip intermittently contacts the sample surface; and E. while the deviceis at the imaging position: a. controlling a separation distance betweenthe sample surface and the device in a manner which maintains thedisplacement amplitude in general agreement with a demanded displacementamplitude, the separation distance being in a direction predominantlyperpendicular to the sample surface, the demanded displacement amplitudebeing lower than the operative/closed-loop resonance amplitudeultimately established at the reference position, and b. impartingrelative motions between the sample surface and the device in a planepredominantly parallel to the sample surface to raster scan the samplesurface.
 51. A method in accordance with claim 50 further comprising thesteps of: A. measuring a phase of the displacement signal with respectto a reference signal while imaging the sample surface; and B. formingspatially-correlated images derived from 1) the separation distance, 2)a discrepancy between the displacement amplitude and the demandeddisplacement amplitude, and 3) the phase.
 52. A method in accordancewith claim 50 wherein the step of adjusting the gain function causes theoperative/closed-loop quality factor to be at least one order ofmagnitude higher than the inherent/open-loop quality factor.
 53. Amethod in accordance with claim 50 wherein the step of placing thedevice at the reference position places the tip in a liquid, wherein thestep of adjusting the gain function tends to negate an effect of dampingimparted by the liquid, and wherein the step of placing the device atthe imaging position places the tip in the liquid.